The intuition is that randomized methods can produce efficient, unbiased approximations of nonrandom operations while being numerically efficient to implement by exploiting modern computational architectures such as parallelization and streaming. The RNLA framework we follow (see [1]} for sketching-based alternatives, or [2]} for random column sampling approaches) is a three step process  [3]}. First, sample the range of the target matrix by carrying out a sequence of matrix-vector multiplications, where the vector is an ensemble of random variables. Next, an approximate low-dimensional basis for the range is computed. Finally, an exact matrix factorization in the low dimensional subspace is computed. The performance of the randomized SVD (RSVD) has been studied in many works [4]}, [3]}, [6]}, [7]} and has found applications in large-scale problems across machine learning [8]}, statistics [9]}, and signal processing [10]}.
